TopTimeNet: Topologically-assisted time-series classification model
Abstract
Distinguishing periodic from chaotic dynamics in a time series is a fundamental challenge in both physics and engineering. Yet, end-to-end learned architectures must discover both a representation and a decision boundary from data, at substantial cost. We introduce TopTimeNet, which decouples these tasks: a fixed, non-learned stage extracts a $42$-dimensional geometric and topological descriptor from Takens delay embeddings and persistent homology, and a lightweight learnable stage performs classification. On a benchmark of $49$ nonlinear dynamical systems, a 1,638-parameter configuration matches the mean accuracy of one with 33× more trainable parameters. Additionally, this approach delivers mean accuracy comparable to convolutional neural networks and surpasses the average performance of converged Transformer models, while requiring three to four orders of magnitude fewer trainable parameters. Robustness also depends sharply on where noise is introduced: TopTimeNet degrades gracefully under perturbations to its precomputed features, but degrades sharply when noise is introduced into the raw signal and the full feature-extraction pipeline is recomputed, showing that robustness to perturbations of the precomputed features does not imply robustness of the complete raw-signal-to-prediction pipeline. These results show that decoupling fixed geometric and topological feature construction from a lightweight discriminative stage can achieve comparable classification accuracy with substantially fewer trainable parameters.
Related
- ChorusTIC: Training-Free Multivariate Time Series Classification via Chorus In-Context Learning
- PU classification under Non-SCAR: clustering-assisted logistic model with oversampling enhancement
- Generalized Linear Mixed Models for Changepoint Analysis of Biomedical Time Series Data
- Continuous Delayed-Memory Stochastic Gradient Descent and Continuous-Time Reinforcement Learning from History of Astrophysical Time Series Studies
- Latent Inference-Time Guidance of Time Series Foundation Models
BibTeX
@misc{sayyad2026toptimenet,
title = {{TopTimeNet: Topologically-assisted time-series classification model}},
author = {Sharareh Sayyad and Sophia Bazzi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39792},
eprint = {2609.39792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39792},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - TopTimeNet: Topologically-assisted time-series classification model
AU - Sharareh Sayyad
AU - Sophia Bazzi
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.39792
UR - https://arxiv.org/abs/2609.39792
AB - Distinguishing periodic from chaotic dynamics in a time series is a fundamental challenge in both physics and engineering. Yet, end-to-end learned architectures must discover both a representation and a decision boundary from data, at substantial cost. We introduce TopTimeNet, which decouples these tasks: a fixed, non-learned stage extracts a $42$-dimensional geometric and topological descriptor from Takens delay embeddings and persistent homology, and a lightweight learnable stage performs classification. On a benchmark of $49$ nonlinear dynamical systems, a 1,638-parameter configuration matches the mean accuracy of one with 33× more trainable parameters. Additionally, this approach delivers mean accuracy comparable to convolutional neural networks and surpasses the average performance of converged Transformer models, while requiring three to four orders of magnitude fewer trainable parameters. Robustness also depends sharply on where noise is introduced: TopTimeNet degrades gracefully under perturbations to its precomputed features, but degrades sharply when noise is introduced into the raw signal and the full feature-extraction pipeline is recomputed, showing that robustness to perturbations of the precomputed features does not imply robustness of the complete raw-signal-to-prediction pipeline. These results show that decoupling fixed geometric and topological feature construction from a lightweight discriminative stage can achieve comparable classification accuracy with substantially fewer trainable parameters.
ER -